Preheat oven to 400 degrees F and prepare a pie dish with olive oil spray or butter.
Peel sweet potatoes and slice thinly. Lay potato slices out in pie dish in a crust-like fashion, spray with oil, and bake for about 15 minutes or until the potatoes are slightly soft. Remove from the oven and reduce temperature to 375 degrees.
Heat a large saute pan over medium heat. Add the tablespoon of butter. Once melted, add the shallot and cook until transparent, about 5 minutes. Add the garlic and spinach, tossing until spinach is wilted and tender, about 4 minutes. Drain off the water released from the spinach.
Whisk eggs in a medium bowl. Then stir in the mozzarella and goat cheeses.
Combine the spinach mixture with the egg and cheese mixture. Add salt and pepper to taste. Pour the combined mixtures into the crust. Sprinkle with parmesan cheese on top.
In a 375 degree oven, bake until the quiche is firm and the cheese has browned, about 40 minutes.